Gauss-PSO algorithm for too short arc initial orbit determination for groud spot

The paper presents a new approach for the Initial Orbit Determination (IOD) from short observations of Resident Space Objects (RSOs). The work is in the framework of the development of the system SPOT promoted by the Italian Space Agency. The system SPOT (Star sensor image on-board Processing for orbiting Objects deTection) is composed by On-board SPOT, to detect potential RSOs from the on-board processing of star sensor images against the fixed stars, and the Ground SPOT which receives the observation data to perform the orbit determination and tracking of the RSOs. SPOT is a suitable system to detect small RSO (< 7 mm) that usually cannot be detected by ground-based observations. Due to the relative dynamics between the orbital observer and RSOs, an orbiting object appears as a streak in the star sensor image. As a result, the observation is a too short arc, which makes difficult to solve the initial orbit determination. The paper studies the IOD algorithm of Ground SPOT by devising a modified Gauss' Algorithm for space-based observer. Knowing the orbit of the observer, the measurements of the lines of sight of a RSO are used to find the state of the target orbit by the Particle Swarm Optimization (PSO) technique. The PSO is implemented in order to find the solution by minimizing a suitable cost function of the lines of sight. The developed algorithm it is able to provide a close estimate of the true state of the observer using too short arcs and it can autonomously choose a root of the Gauss' eighth grade equation.